November 13, 12:45pm, Room 104 Stuart Building
Observational datasets are abundant. Dynamical systems are mathematical models in engineering, medicine and science. Data are noisy and dynamical systems are often under random fluctuations (either Gaussian or non-Gaussian noise).
The interactions between data science and dynamical systems are becoming exciting. On the one hand, dynamical systems tools are valuable to extract information from datasets. On the other hand, data science techniques are indispensable for understanding dynamical behaviors with observational data.
I will present recent progress on extracting information like the most probable transition pathways, mean residence time, and escape probability from datasets, and on estimating system states and parameters with help of datasets. In addition to highlighting the underlying dynamical systems structures, such as stochastic flows, slow manifolds and dimension reduction, I will outline several mathematical issues at the foundation of relevant machine learning approaches.